Exponential convexity, Euler-Radau expansions and Stolarsky

Abstract. We use Euler and Radau two-point formulas in order to generalize Cauchy means defined in [5] that are closely related to Stolarsky means. The gain of this approach is twofold. First, we are able to construct exponentially convex functions that are an essential ingredient of our new means since this fact leads to proof of monotonicity of constructed Cauchy means. Second, con-structed exponentially convex functions are added as non-trivial to sparse examples of exponentially convex functions since invention of exponential convexity back to 1929